একটি বিচ্ছিন্ন দৈব চলক X এর সম্ভাবনা বিন্যাস নিম্নরূপ হলে k এর মান কত? (Find the value of k from the following probability mass function of a random variable X.)x12345P(x)0.22 k0.15k0.3

একটি দৈব চলক X এর জন্য Var (2x + 5)-এর মান কত? (For a random variable X, what is the expression of Var(2x+5)?)

ক

4Var(X) + 5

খ

Var(X)

গ

2Var(X)

ঘ

4Var(X)

What is linear_congruential_engine? for some w using Mersenne Twister algorithm b) Pseudo-random number engine that generates random unsigned integers c) Pseudo-random number engine that generates random unsigned integers in the range for some w using lagged Fibonacci generator d) Pseudo-random number engine that generates random signed integers in the range for some w using Mersenne Twister algorithm

ক

Pseudo-random number engine that generates random unsigned integers in the range for some w using Mersenne Twister algorithm

খ

0, 2w-1

গ

0, 2w-1

ঘ

0, 2w-1

What is the monoisotopic and average mass of valine? Given data: Mass of the most abundant isotope of Carbon (C°)=12.0000, Mass of most abundant isotope of Hydrogen (H°)=1.0078, Mass of most abundant isotope of Oxygen (O°)=15.9949, Mass of most abundant isotope of Nitrogen (N°)=14.0031, The average mass of Carbon (C)=12.011, The average mass of Hydrogen (H)=1.008, The average mass of Oxygen (O)=15.999, The average mass of Nitrogen (N)=14.007.

ক

99.068 and 99.2361

খ

99.216 and 99.326

গ

99.111 and 99.321

ঘ

99.068 and 99.132

চলক x-এর উপর চলক y-এর নির্ভরাংক 1.5 হলে, x-এর মান 2 একক পরিবর্তনে y-এর মান গড়ে কত একক পরিবর্তিত হবে ?

ক

3.5

খ

0.5

গ

3.0

ঘ

0.75

Arrange the following steps in sequence in order to calculate the probability of an event through Naïve Bayes classifier. I. Find the likelihood probability with each attribute for each class. II. Calculate the prior probability for given class labels. III. Put these values in Bayes formula and calculate posterior probability. IV. See which class has a higher probability, given the input belongs to the higher probability class.

ক

I → II → III → IV

খ

II → I → III → IV

গ

III → II → I → IV

ঘ

II → III → I → IV

An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is the same.
If the probability that the face is even given that it is greater than 3 is 0.75, which one of the following options is closest to the probability that the face value exceeds 3?

ক

0.453

খ

0.468

গ

0.485

ঘ

0.492

কোন ছাত্রাবাসে 60% ছাত্রের ইন্টারনেট ব্যবহারের সুযোগ আছে। 4 জন ছাত্রের একটি দলকে দৈব চয়নের (Randomly) ভিত্তিতে বাছাই করা হলে কমপক্ষে 0 জন ছাত্রের ইন্টারনেট ব্যবহারের সম্ভাবনা (Probability) কত?

ক

0.0256

খ

0.35395

গ

0.35392

ঘ

0.45392

The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect.
Statement I The probability of the joint occurrence of independent events A and B is equal to the probability of event A multiplied by the probability of event B or vice-versa.
Statement II The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditionalprobability of event B when event A has occurredor vice-versa.

ক

Both statements are correct

খ

Both statements are incorrect

গ

Statement I is correct while Statement II is incorrect

ঘ

Statement I is incorrect while Statement II is correct

The graph of a function f(x) is shown in the figure.

For f(x) to be valid probability density function, the value of h is

ক

$$\frac{1}{3}$$

খ

$$\frac{2}{3}$$

গ

1

ঘ

3

A probability distribution with right skew is shown in the figure.

The correct statement for the probability distribution is

ক

Mean is equal to mode

খ

Mean is greater than median but less than mode

গ

Mean is greater than median and mode

ঘ

Mode is greater than median